Abstract
Such determinations of representatives have been studied by A. and C. Ionescu Tulcea [2] who call them liftings of L*(R). The theorem of von Neumann has been extended to general finite measure spaces by D. Maharam [1]. Since L*(R) is a commutative Banach algebra, it is clear that a lifting assigns to every real x a multiplicative linear functional, viz. F_(J) =f*(x). The null space of this functional is necessarily a maximal ideal, and since a neighborhood of the unit element consists exclusively of invertible elements, that ideal is not dense, and is therefore closed. Thus the multiplicative linear functional is continuous, and the lifting can be written
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